1) Consider the first table on the web page http://www.johnstonsarchive.net/other/quake1.html titled World Earthquakes, 1970-2012

Looking at the column which lists earthquakes of magnitude 7.0-7.9:

a) What is the average number of earthquakes of this magnitude per year

b) Modelling this as a Poisson distribution, what is lambda?

c) Calculate the probabilities of 
0-5 quakes/year
6-10 quakes/year
11-15 quakes/year
16-20 quakes/year
21-15 quakes-year

d) Fill in the following table:
                                 |  0-5 | 6-10 | 11-15 | 16-20 | 21-25
=======================================================================
  i)Number of years              |      |      |       |       |  
 ii)measured probability         |      |      |       |       |
iii)calculated probabilities (b) |      |      |       |       |
 iv) iii - ii                    |      |      |       |       |

e) Find the mean and s.d. of lines iii) and iv)

2) Given a continuous cumulative distribition function given by:

F(x) = (pi/2 + arctan(x))/pi

a) in order to actually be a cumulative distribition function, what values must
F(-infinity) and F(infinity) take on?  Does this function qualify?

b) what is the corresponding probability density function? (Feel free to look up the
answer)

c) what is the probability that x > 0?

d) what is the probability that -1/2 < x < 1/2?